What is the value of sin(30)cos(60)+cos(30)sin(60) ?

The value of sin(30)cos(60)+cos(30)sin(60) is 1

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sin(30)cos(60)+cos(30)sin(60)

sin (3 0^{\circ}) cos (6 0^{\circ}) + cos (3 0^{\circ}) sin (6 0^{\circ})

1

Solution steps

sin (3 0^{\circ}) cos (6 0^{\circ}) + cos (3 0^{\circ}) sin (6 0^{\circ})

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

Use the following trivial identity:

cos (3 0^{\circ}) = \frac{3}{2}

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

= \frac{1}{2} \cdot \frac{1}{2} + \frac{3}{2} \cdot \frac{3}{2}

Simplify

\frac{1}{2} \cdot \frac{1}{2} + \frac{3}{2} \cdot \frac{3}{2} : 1

= 1

\frac{tan ( 2 5 ^{\circ} ) + tan ( 5 ^{\circ} )}{1 - tan ( 2 5 ^{\circ} ) tan ( 5 ^{\circ} )}

arctan (14)

arctan (15)

(sec^{2} (5 3^{\circ}) + tan (3 0^{\circ})) cot (3 7^{\circ}) - 2 cos (3 0^{\circ})

cot (- 22 5^{\circ})

What is the value of sin(30)cos(60)+cos(30)sin(60) ?
The value of sin(30)cos(60)+cos(30)sin(60) is 1